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EXISTENCE OF ALMOST SPLIT SEQUENCES VIA REGULAR SEQUENCES
Published online by Cambridge University Press: 18 March 2013
Abstract
Let $(R, \mathfrak{m})$ be a Cohen–Macaulay complete local ring. We will apply an inductive argument to show that for every nonprojective locally projective maximal Cohen–Macaulay object
$ \mathcal{X} $ of the morphism category of
$R$ with local endomorphism ring, there exists an almost split sequence ending in
$ \mathcal{X} $. Regular sequences are exploited to reduce the Krull dimension of
$R$ on which the inductive argument is established. Moreover, the Auslander–Reiten translate of certain objects is described.
MSC classification
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 88 , Issue 2 , October 2013 , pp. 218 - 231
- Copyright
- Copyright ©2013 Australian Mathematical Publishing Association Inc.
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